The main epoch of activity for active galactic nuclei appears to have been z ~ 2. Until very recently, the suspected symbiotic link between star formation, galaxy mergers and nuclear activity led people to believe that star formation activity in the Universe also peaked at z ~ 2, despite the failure of searches to find a primeval galaxy at z >1. When a large population of star-forming galaxies was finally discovered at z > 2, the astronomical community believed it had entered a new era of understanding how and when most of the stars of the Universe were formed. However, the star-formation rates observed in these systems are relatively modest, a few tens of solar masses per year, and are unable to build a massive elliptical galaxy in anything less than a Hubble time. Furthermore, the stellar populations in local massive ellipticals appear to have been formed in a short-lived, violent, dusty starburst at high-redshift, although it is not clear whether the formation trigger is a galaxy merger or the collapse of a huge halo of gas. The large quantities of dust that are expected during formation will absorb the optical/ultraviolet emission of the young stellar population and re-emit it in the far-infrared waveband. Locally, all powerful radio sources reside in massive elliptical hosts. It is therefore natural to assume that high-redshift radio galaxies are the progenitors or earlier examples of these local systems. This thesis presents a study of the evolution of dust and gas (and hence star formation) in massive ellipticals. A sample of 47 luminous, steep-spectrum, lobe-dominated radio galaxies spanning a wide range of redshifts, 0.77 < z < 4.41, has been observed with SCUBA, a submillimetre camera on the James Clerk Maxwell Telescope. SCUBA observations are particularly well-suited to this study: the dust emission expected during star-formation episodes at early epochs will be redshifted into the submillimetre waveband, and the strong negative K-correction associated with the dust emission spectrum overcomes cosmological dimming, i.e. SCUBA is as sensitive to radio galaxies at z = 1 as it is to radio galaxies at z = 4. Observations were carried out at 850 mm and 450 mm simultaneously, to a uniform depth of 1 mJy at 850 mm. Given the negative K-correction, the entire sample was observed to roughly the same depth in 850-mm luminosity. Careful corrections for synchrotron contamination from the radio source at submillimetre wavelengths have been made. The submillimetre emission could potentially be linked to either radio luminosity or redshift or both. In order to decouple these two effects and determine if the sample truly exhibits evidence for the cosmological evolution of dust and star formation. The sample has been chosen to span a large range of redshift but a narrow band of radio luminosity. For the radio galaxy sample, as one moves to higher redshifts there is a startling increase in the detection rate at 850 mm. Having removed the radio luminosity bias, the 850-mm luminosity of the sample is found to increase steadily between z ~ 1 and z ~ 4.5, indicating that the main era of star-formation activity in massive ellipticals was at z 4.